TABLE 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Table 9-9, the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.

Using a two-tailed t-test with a sample size of 20 and a sample mean of 1,501, we can calculate a t-value of -2.63. With 19 degrees of freedom and a 5% level of significance, the critical t-value is +/- 2.093. Since our calculated t-value of -2.63 is less than the critical t-value of -2.093, we reject the null hypothesis that the mean SAT score for this year's entering class is equal to or greater than the mean SAT score for previous years, and conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.

TABLE 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Table 9-9, which of the following best describes the Type I error? A) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. B) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher. C) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower. D) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

Type I error occurs when the null hypothesis is rejected when it is actually true. In this scenario, the null hypothesis is that there is no significant difference between the mean SAT score of this year's entering class and previous years. If the president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower, he is committing a Type I error by rejecting the null hypothesis when it is actually true.

TABLE 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Table 9-9, if these data were used to perform a two-tail test, the p-value would be 0.1254.

Since the question mentions a two-tail test, we can find the p-value by looking at the row in Table 9-9 that matches the sample size (n = 20) and the corresponding t-value for a two-tail test with 19 degrees of freedom (df = n-1). In this case, the t-value is -1.729, which corresponds to a p-value of 0.1254. This means that if we were to perform a two-tail test at a significance level of 5%, we would fail to reject the null hypothesis that the mean SAT score for this year's entering class is not significantly different from the mean SAT score for previous years. Therefore, the answer is A, true.

TABLE 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Table 9-9, the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

The answer of TABLE 9-9 The president of a university claimed...

TABLE 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Table 9-9, which of the following best describes the Type II error? A) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. B) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher. C) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower. D) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

A Type II error is when the null hypothesis is not rejected when it is actually false. In this case, the null hypothesis is that the mean SAT score for this year's entering students is equal to or greater than the mean SAT score for previous years. Therefore, a Type II error would be if the president concludes that the mean SAT score of the entering students is not lower than previous years when it is actually lower.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests

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